2-digit lists

Discrete Mathematics Level pending

An list of increasing two-digit positive integers is formed so that

-each integer in the list uses only digits from \({1, 2, 3, 4, 5, 6}\)

-each of the integers in the list has its units digit is greater than its tens digit, and

-each of the digits \({1, 2, 3, 4, 5, 6}\) appears in exactly three of the integers in the list.

How many different lists are possible?

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